Dynamic Response Of Multi-Span Continuous Bridge With Considering Of Vehicle-Bridge Coupling Effect

With the gradual development of modern bridges in the direction of large span,flexibility and multi-functionality and the popularization of vehicles,the coupling vibration problem of vehicles and bridges has become increasingly prominent.The vehicle-bridge coupling problem based on vehicle load has also attracted more and more attention from scholars and engineers at home and abroad.At present,the research on influencing factors of bridge dynamic response mainly focuses on irregular time-varying loads such as wind load and seismic load,while the research results on dynamic response of continuous beam under moving load are less.This paper analyzes the stress of the bridge under the action of single vehicle and multiple vehicles,and then studies the coupling response of single vehiclecontinuous girder bridge and the coupling response of multiple vehicles-continuous girder bridge.Firstly,based on the Euler-Bernoulli continuous beam theory,the piecewise solution idea and the separation of variables method are adopted in this paper.Based on the boundary conditions between beams and the continuity conditions of force and displacement,the vibration mode function of the corresponding beam segment and the relationship matrix of its undetermined coefficients are established in segments,and the total relationship matrix of the vibration mode function of the continuous beam model with arbitrary spans is solved.Then,the natural frequency and vibration mode function of the multi-span continuous beam with equal section are solved by the semi-analytical method.In the second place,the 1/4 vehicle model and the nonlinear model of the bridge considering the suspension system are studied in depth.The vehicle-bridge coupling vibration control equation of the continuous beam bridge coupled with the vehicle and the bridge is derived by using the Hamilton variational principle.The dynamic response of the bridge at any position of the bridge is solved by using the fourth-fifth order Runge-Kutta method.The accuracy of the established single vehicle-continuous beam bridge coupling motion balance equation is verified by comparing with the example.Then based on the vehicle-bridge coupled vibration equation,taking three-span continuous beam as an example,the influence of vehicle speed,body mass and tire stiffness on the displacement response of vehicle-bridge coupled vibration bridge is analyzed.The research results show that the vertical displacement in the middle of the bridge span will also change with the change of the vehicle speed.The influence of body mass and wheel stiffness on bridge mid-span displacement response is not obvious.The last but not least,based on the above research conclusions,the vehicle-bridge coupled vibration analysis model under the action of multiple vehicles is established and solved,and the influence of the distance between two vehicles and the vehicle speed on the dynamic response of the bridge is studied when the vehicle runs at a constant speed on the bridge.